87 by yantingting


									                                                       The Psychology of Risk:
                                                           A Brief Primer

                                                          Paul Andreassen*

                                                        Working Paper No. 87

                                                             March 1993

*The Jerome Levy Economics Institute of Bard College
            Risk is commonly       defined in negative terms--the       probability   of suffering loss, or factors and actions involving

uncertain      dangers or hazards.      In contrast, the definition    used in the social sciences relies on simply the degree of

uncertainty--how       much variance exists among the possible outcomes associated with a particular                     choice or action.     Counter

to intuition,    an investment     that will lose $5 for certain would therefore be classified as less risky than one that has an

equal chance of yielding either a gain of $10 or a gain of $15.                 Uncertainty     and value are treated as separable entities

because expanding        the notion of risk to include gains as well as losses adds considerable                conceptual    power.   For example,

depending       on how a pair of options is described,       a choice can appear as if between two losses or between two gains.

Consider the following:

                 Problem I: Imagine that you are faced with a life or death choice. The U.S. has safely quarantined
            all 600 people infected with an unusual virus, but is now certain that they will all die without some
            treatment. Resources are severely limited and the choice mast be made between two scienttjk programs.

                 Program A: If adopted,       2cO people will be saved for certain.

                 Program B: If adopted, there is a IN probability             that 600 people will be saved and a 2/3 probability
            that no people will be saved.

People choose A over B by a ratio of three to one, showing a preference                   for the certain outcome.           Now consider the same

scenario with a different set of choices.

                 Program C: if adopted, 400 people will die for certain.

                Program D: If adopted, there is a l/3 probability             that no people will die and a 213
            probability that 600 people will die.

People choose D over C by a ratio of four to one, showing a preference                    for risk.       However,    note that the end results of A

and C are exactly the same--200 people alive, 400 dead--as are those of B and D.                          According   to classical theories of

rationality,    one cannot both prefer A to B and D to C. This paper will discuss why most people do.

            Economic    theories based on “perfect” rationality         are undoubtedly       powerful.     If one wanted to describe or predict

human behavior in the simplest possible manner,             one would certainly want to begin by assuming                (1) that people are

motivated by their own self interests,         and (2) that they can be extremely calculating              when valuable opportunities       arise,

learning quickly from the success of others.            Research on the psychology         of risk does not begin by assuming          that all

human behavior        is irrational,   random, or thoughtless.        Rather this research has centered on how people may be biased by
various social influences,       by the way that they perceive the choices available,         or by the cognitive      rules of thumb that they

use to simplify difficult decisions.

                             I. SOCIAL        INFLUENCES       ON JUDGMENTS            OF RISK AND CONTROL


          In principle,     the distinction   between skill and luck would seem clear.           Skill situations are characterized    by a causal

link between behaviors         and outcomes.     Success in skill tasks is controllable,    whereas success in a chance activity is not.

Yet the distinction       is often not recognized.     ln a series of essays and studies, Ellen Langer showed how people often treat

a chance event as if it involved skill and was therefore under their own control.                  Studies conducted     in Las Vegas casinos

have found that a dealer who experiences             a run of bad luck risks losing his or her job.          Dice players often concentrate

carefully on the outcomes they desire, throwing their dice harder when they need higher numbers                        and tenderly when low

numbers are required.          Langer argued: “by encouraging         or allowing participants     in a chance event to engage in behaviors

that they would engage in were they participating             in a skill event, one increases the likelihood       of inducing   a skill

orientation;   that is, one induces an illusion of control.           By introducing   choice, familiarity     with [the situation],   active

involvement,     or competition      into a chance situation where people cannot influence           the outcome, they will show behavior

more appropriate      to a skill event.”

          Several lotteries conducted by Langer are telling as to power of the illusion of control.                   ln the first study, Langer

assessed the effects of choice, using randomly           determined     subjects who worked at two business offices in which drawings

and sports pools were common.              The experimental    procedure was straightforward.         Potential customers     were approached

and asked if they would like to buy a lottery ticket.            The assistant explained that about fifty tickets in total were being

sold, each costing $1.         They were told the date of the drawing that would determine             who won the entire pool.         It being

football season, the lottery tickets were two matched sets of standard football cards, each card with a picture of a famous

player, his name and his team.           Both sets were arranged first by team and then by the player’s name.                After agreeing to

play, the first customer was given one of the sets and asked to select one of the cards.                   The customer named the card so

that the assistant could fii       the matching card from the other set, drop it into a sealed carton, and make a note of the

customer’s     name and card.       The next customer was treated in the same way, except that after agreeing to play, they were

handed a card that matched the choice of the preceding              subject.   Repeating this process, people were alternately             placed in

the choice and the no choice condition.        The important test came on the morning               the lottery was to be held.      The assistant

approached    each of the customers individually       and explained:    “Someone in the other office wanted to get into the lottery,

but since I’m not selling tickets any more, he asked me if I’d find out how much you’d sell your ticket for.                         It makes no

difference to me, but how much should I tell him?”

         Choice dramatically      increased the value of the ticket.        Customers     in the choice condition        required an average of

$8.67 before they would sell their tickets, in contrast to an average of only $l.%                   in the no choice condition.        The

customers were oblivious        to the effect, and not one of the subjects was willing to admit that either choosing or not

choosing their card would have changed their selling price.             However,     many states have spent considerable           funds so that

people playing the lottery would be able to pick their own numbers.

         In a second study, Langer demonstrated          powerful effects of familiarity       on the illusion of control.         Again there

were two groups of customers.         In this study both groups were allowed to choose their own tickets.                    However,    one group

chose from cards identified by numbers,        whereas the other group chose from cards identified by undecipherable

hieroglyphics.      Customers   holding cards with the unfamiliar       symbols agreed to sell back their tickets for substantially              less

than did those holding cards with familiar numbers.

         This work would appear to have several implications             for the psychology         of investment,     in which uncontrollable

factors significantly    affect one’s final outcome.    For example, research has shown that people overestimate                   their own

control (i.e., underestimate     risk) when given the opportunity       to purchase a familiar option.          Because people are generally

highly familiar with their own company,        they may be prone to under-appreciate            the full degree of risk that occurs if they

concentrate      their security holding in the company’s    stock, as nearly half of all individual          investors do.     Both their salary

and their savings then depend upon the health of a single company.                 This research may also help explain why stock

trading volume tends to plunge following insider scandals, as it did during World War I, the early 193Os, and in the latter

half of the 1980s.      Langer showed that people bet less against a dapper, well spoken player than against a player looking

disheveled and boorish (in her words, a “snook”) even though in both cases the outcomes of the gamble were determined

by tossing a coin.      Realizing that one may be facing more sophisticated             opponents    is likely to reduce the illusion of

control, thus decreasing     the ease with which people will accept risk, even if the disadvantage                   is more illusory than real.


          Among the most famous studies in social psychology             are those that concern the effects of groups on decisions

concerning      risk.   This research began in the early 1960s using problems previously                 employed to assess individual

differences     in risk taking.    Each “choice dilemma” described a situation in which an individual                is presented    with an option

between a moderately         attractive certain alternative,   and a risky one that potentially      has greater promise.        For example:

              Problem 2: Bob is playing chess in a tournament against a much stronger player. If he follows his
         present strategy he ts certain to achieve a draw. Suddenly, Bob realizes that there is an alternate strategy
         that, tf it succeeds, will quickly win the game, but will lead to sure defeat tf not.

              Imagine that you are advising Bob. Listed below are several probabilities of the alternate strategy
          working. Please check the lowest probability that you would consider acceptable to make it worthwhile
         for Bob to choose the alternate strategy.

                 fl I in 10 that the alternate strategy will succeed
                 /j 2 in 10 that the alternate strategy will succeed
                                    . . . .. . . . .
                                    . . . .. . . . .
                 fl 9 in 10 that the alternate strategy will succeed
                 fj Bob should not choose the alternate strategy, no matter what the probabilities.

People read the dilemmas          and made their initial choices.      Some subjects then met in groups, discussed the problems

among themselves,         and again made private choices.        With the original set of problems,          after discussion   a clear majority of

subjects later privately chose more risky options.             Subjects given no chance to discuss did not systematically             change their

private views.

         The effect of group discussion          was first called the “risky shift,” but continued          work made it clear that this was an

incorrect name.         Some choice dilemmas consistently        produce caution shifts.     Such effects commonly          occur when the risky

option involves the possibility        of ruining one’s life, severely harming others, or dying.             When people are initially

conservative,     finding the risky option acceptable only if its odds of success are very high, then after discussion                  they

become even more conservative,            becoming   even less willing to accept w         probability     that the risky option will fail.     The

phenomenon        has been more aptly named the “group polarization”             effect because the shift can be either toward risk or

toward caution, generally         reflecting the initial biases of the individual    discussants.    Group discussion       has been described

by one European researcher          as acting like a developer on exposed film: “it brings out the picture, but the outcome is

predetermined.      ”

         Group polarization        is not due to greater powers of leadership in those who advocate the extremes,                   or due to

pressures to conform.         Rather, the polarization    effect is caused by social comparison           and the number of arguments         pro or

con presented during discussion.          First, befor e h earing the Positions of others, people generally believe that they have

answered in a more desirable          fashion than most others would.          Since not everyone can be better than average, group

discussion    generally    provides people with surprising       information    as to what constitutes     a socially ideal level of risk or

caution, causing an impetus to polarize in the favored direction.                   Second, the initial individual     leanings toward risk or

caution generally      reflect the pool of arguments          that will arise during discussion.        Given that with most problems not

everyone will have thought of all of these arguments,                 the difference between the number of arguments               in favor or against

risk is likely to widen during discussion,             favoring the initially preferred pole.         People are strongly swayed by new

arguments      in favor of a particular      position.     As one would expect, little movement           is caused by discussion       of highly

familiar issues.

             Two findings regarding       group polarization       may be particularly     relevant to financial    investments.      First, research

has shown that the direction          of the shift due to discussion      depends on the magnitude          of the investment.       After discussion,

people become more risky with small stakes, but more conservative                       when the stakes are large.      Second, the shift toward

risk due to discussion          has been found to increase as the difference between the expected return of the risky alternative                     and

the certain outcome expands.            Combining        these two findings,     one would expect that the acceptability         of a small position in

a high-growth,      high-risk instrument          is likely to rise after an investor is given time to “talk it over. ”


             The accepted psychiatric       description     of mania includes not only elevated mood, self-esteem            and energy, but also

“excessive involvement           in pleasurable     activities that have a high potential for painful consequences,          [such as] buying

sprees,...     and foolish business      investments. * These symptoms aptly describe those shown across much of England during

the South Sea Bubble of the 1700s and the U.S. during the 1920s.                       (Clinical wisdom is that a manic must never be given a

credit card.)      Similarly,     economic depressions        share the common clinical symptoms of indecisiveness,                apathy, and loss of

energy.      Because many factors act so as to affect people’s moods at the aggregate level, the clinical literature                       on mania

and depression      can help predict aggregate changes in investment                preferences.

             People strive to nurture positive moods.            Consequently,     elevated mood causes steeper demand functions              for

increasingly     positive returns and for greater probabilities          of return.     Surprisingly,    research has also shown that elevated

moods are also characterized           by a greater propensity       to buy insurance     against large losses.     Positive moods are something

people are willing to pay to protect.              However,    positive moods reduce the extent to which people accurately               assess their

own exposure to risk.           Positive mood states lead people to examine fewer of the variables related to a particular                    decision,

to pick these variables         more quickly, and to process these few pieces of information               more thoroughly.         The three effects

lead to overconfidence          in their own decisions,       because contradictory     information     is less likely to be uncovered      and any

that does arise is more likely to be assimilated.                 Positive moods induce the illusion of control, causing people to have great

difftculty recognizing         when the connection         between their own actions and any rewards they receive is missing.                            Manics

credit themselves       for all good things that happen.                In contrast, depressives      do not suffer from this illusion,          and are readily

able to distinguish      between circumstances            in which their actions are effective and those in which they are not.                         Negative

mood states lead to an exhaustive examination                   of the variables,     and to very long decision times.

             At the aggregate level, positive moods would be expected to draw people toward high risk investments.                                        By

examining      fewer of the potentially         important     sources of information          available,     investors are more likely to fail to realize

the complexity       of the information        that must be mastered to successfully              employ a given asset.           In contrast, negative mood

states at the aggregate levels increase the likelihood that investors become unable to make decision,                                   becoming       paralyzed

while attempting       to process all of the complex information                 available.     General dysphoria is also likely to increase

investors’     willingness     to accept low rates of return.


             What is the underlying          motivation    for actions that occur even when there are no immediately                      compelling      external

or physiological      forces?      What causes intrinsic motivation             to persist or diminish. 7 There are two common characteristics

of freely chosen activities.          First, by engaging in the behavior,             the individual        must gain some opportunity         to evaluate his

or her performance.            Second, the behavior must be freely chosen, and not forced by some extrinsic                             threat or promised

reward.       Surveillance,     deadlines,    and rigidly held standards and requirements                   all significantly    reduce the extent to which

people will engage in an activity if left to themselves.                     These simple facts can explain some seemingly                  paradoxical

behavior.      For example, blood donation in England actually increased when hospitals stopped paying for blood.                                         Payment

reduced the extent to which people could provide themselves                        with positive feedback, defining              their gift as having been a

moral act untainted          by extrinsic control.        Similarly,     in the 196Os, families covered by private pension plans voluntarily

saved greater amounts of money than families that were not.                         (Controls were included for age, income level, geographical

area, and the like.)          The former did not need to save to enjoy a comfortable                       retirement,   and could enjoy their increasing

their savings as a freely chosen positive behavior.

            Drawing upon this work, several factors would seem likely to increase investors’                               intrinsic motivation        to change

their investments.       First, the initial decision to invest may be facilitated if people understand                          that their financial    position

does not reouire them to make these investments,                       but rather that it is a freedom that their financial            situation provides.
Second, investors may become more motivated to trade to the extent that they believe that doing so is likely to provide

them with meaningful        performance   feedback, information   which allows them to assess and improve their own skills.             To

receive such feedback, investors need to believe that they personally          have actively made informed choices, because then

they will be able to attribute their performance      to themselves    and not to others or to luck.    Several theorists have argued

that investors use full service brokers so that they can have someone else to blame if the investment              goes bad.     ln fact,

investment     advise may be sought so that people feel informed enough to be able to blame themselves.

                                    II. DECISION      THEORY:      UTILITY      AND PROBABILITY


          Decision theories seek to describe how people should choose among sets of potential outcomes.                  These theories

were first constructed      when French nobles in the 18th Century called on their court mathematicians           for help in playing

cards and dice.      We begin with expected value theory, which failed although it often seems intuitively             compelling.    The

expected value of a given choice is calculated by multiplying          the probability   of each potential outcome by its monetary

equivalent,    and then summing     across all of possible outcomes.      ln many cases, people do not use expected values in

making their choices, nor do they think that they should.         The expected value of insurance       is negative,   yet purchasing       it is

not always irrational.      Expected values are also often ignored when given choices between positive outcomes.                Consider

the following problem:

              Problem 3: l7te gamble is determined by tosses of a fair coin. On the first jlip, a tail em& the game and you
         receive nothing, but a head gives $2 and the opportunity to flip again. Every time you Jip another head, your
         cmh prize for that round is double that of the previous one. l%e gamble ends the first time the coin comes up
         tai&. which would your prefer: (A) to play the gamble, or (B) $l,CXW,&W?

The expected value of the gamble, called the St. Petersburg           paradox, is infimite: l/2 x $2 + l/4 x $4 + l/8 x $8 + . . . .

ad infmitum.      People are rarely willing to forgo even $100 to play.

         Bernoulli    argued that people could rationally    reject the St. Petersburg    gamble because there is no reason that

monetary value (i.e., $x) and psychological        utility (i.e., U($x)) need be perfectly related.    (Utility is the economists’      term

for units of satisfaction    or happiness.)   ln fact, because for most people the per dollar increase in utility appears to decline

as dollar values grow larger, utility theory predicts that people are generally risk averse.           Suppose one has a choice

between (A) a certain $10 million and (B) an even chance of $20 million or nothing.               To calculate which option to choose,

one must multiply the utilities of each possible outcomes by the probability              of that outcome,     and then choose the

alternative     that yields the highest sum.      Conse+ently,      the choice in this example depends on which is larger,       1.0 x

U($lOM) or 0.5 x U($O) + U($2OM).                 Most people seem to feel that getting $10 million would make them about as

happy as they can get.         Setting no money to zero utility and $10 million to ten units of utility, $20 million might rate only

a twelve.       If so, then the choice should be Option A (i.e., 10 > 6).           This framework       can also explain why everyone    could

be rational and yet not make the same choices, for it allows different individuals              to have different utilities for money.

            To give utility theory a fum foundation,        several theorists have attempted to derive the theory from a basic set of

assumptions      or axioms.     These commonly       include the following:     Cancellation:   states of the world that will occur

regardless of one’s choice should not affect one’s preferences.               If one prefers A to B, then one also prefers A+Z        to B+Z.

Transitivity:      it is possible to assign each option a value that does not depend on the other available options.             If one

prefers A to B and B to C, then one also prefers A to C. This assumption                  is necessary    so that options can be ordered.

Dominance:        if one choice is better along at least one dimension,        and as good on all of the remaining      dimensions,   then it

will be most preferred.         Invariance:   different descriptions    of the same choice problem should all yield the same choice.

            Although theories of rationality      can be derived from these axioms, none of them describe how people actually

make choices.        For every axiom there is a case in which people’s choices systematically              violate the axiom.   The first case

discovered      is listed below.

            Problem 4: l’he Allais Pam&ox

            Part I: Choose A or B                          Part II: Choose C or D

            Gamble A: 100% chance of $lM                   Gamble C: 11% chance of $IM
                                                                     89% chance of nothing

            Gamble B: 89% chance of $lM                    Gamble D: 10% chance of $5M
                      10% chance of $5M                              90% chance of nothing
                      1% chance of nothing

Most people prefer A over B, wishing to avoid the small chance of getting nothing.                   People also prefer D over C,

showing a willingness         to forgo a slightly higher probability     for a much greater potential reward.       This pattern of choices

violates the cancellation       axiom because subtracting        a 89% chance of $lM from A and from B turns them into C and D,

respectively.      Consequently,     the only rational choices are both A and C or both B and D.             Even utility theorists admit that

they have trouble convincing         themselves    to follow either theoretically   rational course of action.


             The most widely accepted descriptive       theory of choice is Kahneman             and Tversky’s    Prospect Theory, which first

appeared in Econometrica         in 1979.     Many of the problems presented here are variations               of those invented by Kahneman

and Tversky.       There are many components         to the theory, and only the most important              aspects will be described        here.

             According    to the theory, there are three important properties of the psychological               value assessment      process.

First, individuals       view monetary outcomes not in terms of absolute wealth, but in terms of changes from some reference

level, which is often the status quo.          Second, there are not only diminishing           positive psychological    returns for positive

consequences,      but also diminishing      negative psychological    returns for negative consequences.            The difference         between

losing $1 as opposed to $5 is not perceived as severe as the difference between losing $501 as opposed to $505.                                 Finally,

the resulting psychological       value function is steeper for losses than for gains.            Finding    $10 is less of a positive change

than losing $10 is a negative change.           (A graph of a typical value function appears at the end of this paper.)

             The shape of the value function has several important            implications     regarding    people’s choices, all of which have

since been substantiated       by a considerable    body of research.      First, because the value function for losses is convex, people

are typically risk seeking in the domain of losses, the opposite of their behavior in the domain of gains.                          For example,

because losing $200 is generally          not twice as bad as losing $100, most people prefer an even chance of losing $200 or

nothing over a certain loss of $100.           Second, because the curve for losses is steeper than the curve for gains, few people

will accept an equal chance of winning or losing the same amount when the stakes are high.                          Thud, the largest

psychological     change per monetary unit occurs when crossing the threshold between losses and gains.                       The psychological

effects of all other $1 monetary        changes pale next to the one that occurs between losing $1 and breaking                     even.     Finally,

because people often allow their reference points to be shifted by the manner in which the particular                       problem is described,

their choices are often inconsistent        from an objective standpoint.        In Problem       I, people prefer the sure option when the

problem is framed as a choice between two gains (i.e., lives saved), but prefer the risky option when the problem is

framed as between two loses (i.e., lives lost).

             According    to the theory, there are four important characteristics            regarding   how people weight a given probability

when making their decisions.          First, people underweight       moderate and high probabilities.           This contributes     to general risk

aversion for gains and risk seeking for losses.          Second, there is a strong psychological             change from high probabilities              to

certainty.     Consider the following       facetious example.   Suppose you are forced to play Russian roulette, but are offered a

chance to pay to remove one bullet from the gun.             Would you pay more if there were two bullets in the gun or only one?

Although both purchases increase the probability           of living by the same percentage,    most people report that they would pay

much more for the solo bullet, making survival a certainty.            Third, people tend to treat small probabilities      as if they were

equivalent.    People tend to prefer an .8 chance of winning $SK to a .4 of winning             $9K, yet they prefer a .0004 chance of

winning     $9K to a 0.0008 chance of winning $.5K. Not all 2: 1 odds are created equal.             Finally,   there is a tendency to

overweigh     small probabilities.     Consequently,   people are generally risk seeking in the domain of losses, yet wilhng to

insure themselves     against unlikely    disasters.   This aspect of the probability   weight function underlies     the inconsistency

shown in the Allais paradox.          Improbable   gains and losses both loom large.      (A graph of a typical probability      weight

function appears at the end of the paper.)


          Prospect theory divides the decision making process in two parts: a phase during which the available prospects are

“framed” (i.e., put into a particular       perspective)   and edited, and then a phase of evaluation     and choice, which was

described in the previous section.         The first part is controlled by norms and habits as well as the manner in which the

problem is presented.       Different editing processes may occur depending         on how a particular    set of choices is framed,

causing preferences     to shift.    Several such framing effects have been explored.

          First, frames can affect choice by inlluencing        where the reference point is set.    Consider the difference      between

discounts and surcharges.        A price difference    in favor of L(ow) over H(igh) can be framed as an advantage             of L by

making H the neutral reference point or as a disadvantage            of H by making L the neutral reference point.          If L is the

neutral reference point, then the price difference         will be seen as L minus H, that is, as a loss.       If H is the neutral

reference point, then the price difference         will be seen as H minus L, that is, as a gain.     Because the loss function       is

steeper than the gain function,        an identical difference will not be perceived the same in the two different frames.            Consider

what might have happened to the use credit cards if the price difference between credit and cash gas purchases had been

labeled as a credit card surcharge,         rather than a cash discount.

          Setting the reference point can also influence        whether people are risk seeking or averse.        Investment    problems are

somewhat more complicated            than those presented thus far because most risky financial     instruments     are best described by a

continuum     of possible returns rather than by discrete outcomes, but consider the following:

          Problem 5:

             Frame I: An investor is presented with two choices: She can pick either Option A, which is certain to
          make money this year, or Option B, which has a 67% chance of making money this year.

                  Frame II: An investor is presented with two choices: She can pick either Option C, which is certain
            to make less than 15% this year, or Option D, which has a 40% chance of making less than 15 % this

The first frame describes the choice in terms of gains (i.e., returns greater than O%), which would be expected to increase

the preference         for the certain option, say, T-Bills over a portfolio of small firm stocks.        In contrast, the second frame

describes the choice in terms of losses (i.e., returns less than 15X), which would be expected to increase the preference

for the riskier choice, say, a portfolio of small firm stocks over T-Bills.

            Second, frames can make the likelihood of a rare event appear relatively            large by segmenting      the possible causes

of that event into s&components.            For example, the collective decision weight associated with four probabilities           of .Ol

generally     exceeds that of a single probability     of .04 because of the tendency to treat all small probabilities       as equal.

Consider the following          example:

                 Problem 6: You have a chance to buy high yield bonds in a small chemical company. Your return is
            certain unless a leak occurs at the company s plant, in which case liability suits against the company will
            cause you to lose your entire investment.

                 Frame I: “Experts agree that the current probability          of a leak due to all factors   is 4%. ”

                Frame II: “Experts agree that there are four factors that can lead to a leak, each of which has a 1%
            chance of occurring: (i) total failure of the main coolant pump, (ii) cracks in the sealing gaskets caused
            by sudden changes in weather condition, (iii) human operator error, and (iv) malfunction in the electrical
            control system. ”

People weigh the risk of failure higher if the way the system can fail is divided into its subcomponents.                  Further

subdivision     increases the effect (e.g.,    “The main coolant pump can fail due to sudden changes in demand,              an accidental

severing of the wiring, failure of its reserve electrical system, or insufficient          lubricant.“)    This divide and conquer strategy

was effectively used by activists to rally protest against the construction           of new nuclear power plants.

            Finally,     frames can affect choice by making uncertain        outcomes appear certain.     These “pseudo-certainty”       effects

can be made to occur if a problem is described as occurring             in stages rather than solely in terms of the full       outcomes.

This is illustrated       in the next two problems.

            Problem 7:

                 A company is competing for a government contract.              You have the option of receiving one of the
            following two securities:

                 Security A has a 25 % chance of paying $3ooO and a 75% chance of paying nothing.

                 Security B has a 20% chance of paying $4500 and a 80% chance of paying nothing.

Approximately          four out of five people choose Security B.

            Problem 8:

                A company ir competing for a government contract. The probability that the company will not receive
            the contract is 7.5%, in which case both of options below will yield nothing. If the company does win the
            contract, then:

                 Security C will pay $3ooO for certain.

                 Security D hag a 80% chance of paying $4500 and a 20% chance of paying nothing.


Approximately       three out of four people choose Security C. Because there is a 25% chance that the contract will be won,

Security C has a 25% chance of yielding $3000, and Security D has a 20% chance of yielding                            $4500 (i.e., .25 x .80).

Although securities A and C are functionally             identical,    only C is preferred.   The payoff for C appears to be certain,

although it is not, because the frame provided in Problem 8 encourages                   people to ignore the uncertainty       in the initial

stage, which is common to both choices.


            Probabilities    in the problems above are stated precisely,         which is rarely the case in the real world.          Rather,

probabilities     must usually be estimated from a set of noisy and vague variables.               People use many cognitive heuristics,

mental rules of thumb, to make these estimates.                  These heuristics allow estimates to be made rapidly, expending            a

minimum       of cognitive     effort.    The two heuristics that have received the most research attention will be described               here.    Of

the dozens of heuristics that have appeared in the risk literature,              most are variations   of these two.

            1) THE AVAILABILITY                HEUBISTIC:          Judgments of relative frequency     or of the likelihood of a future event

are often made by assessing the degree to which the event is available--perceptually,                  in memory,       or via construction      from

imagination.       This heuristic is often accurate, but there are many factors that are uncorrelated                with frequency    that affect

perceptual      salience, the completeness       with which we recall, or the degree to which something can be imagined.

            The availability     heuristic can lead to biased likelihood estimates because some information               is highly salient.     The

media present biased samples because they must focus on the sensational                   and ignore statistically     frequent (i.e., boring)

events.     Rarity and newsworthiness          are much the same.       However, this biased sample of information          causes people to

overestimate      the frequencies        of uncommon   events.     For example, the media report every suspected case of death by

botulism,    but rarely report death by diabetes.          Although,     the true ratio is approximately     1 to 10,000, research has shown

that the number of deaths per year caused by botulism and by diabetes are commonly                         estimated as being equal.      Similarly,

bankruptcy      of a major corporation        is newsworthy,    but non-bankruptcy     is not.     Even experienced         investors overestimate       the

frequency     with which major corporations          suffer bankruptcy.

            Availability    from memory often leads to overconfidence            in judgment.      Consider the following         question:    Which

company employs more people, Mobil or Chrysler. 9 Even when rewarded for understating                              the probability     that they have

answered correctly,        people greatly overstate the likelihoods that their answers to such questions are correct.                       The

information      one is missing is rarely given sufficient weight in balancing           the confidence judgment.              Memory induced biases

can also occur when reasoning            about a single case.     How does an analyst decide whether a particular                 company is likely to

show high levels of growth?            A common intuitive strategy for making this type of judgment                 is to recall similar cases and

then base the likelihood estimate on the percentage             of these available cases in which there was also high growth.

Unfortunately,      irrelevant     factors can bias retrieval by activating a narrow set of associative            links.     For example,        an

analysis performed         on an the anniversary     of a significant   historical event may lead to high levels of recall from that time

period.     If the economic conditions        that held then are significantly     different from those of the present, biased estimates

would be expected.

            Reasoning      by the use of cases and scenarios is rarely efficient because only a portion of the obtainable                      information

is used.     An effect called the “hindsight” bias appears due to the fact that some scenarios may be much easier to construct

than others.      People consistently       exaggerate   what could have been anticipated         in foresight.    Even recall of past predictions

is systematically     distorted.     The hindsight bias generally occurs because the scenario that one believes led to the actual

event becomes so compelling            that it becomes difficult construct or imagine the alternative             scenarios that would have led to

different outcomes.         This bias causes difficulty     in learning from history.      Success or failure appears inevitable              once the

outcome is known.

            2) REPRESENTATIVENESS.                   The representativeness      heuristic is a cognitive     rule in which judgments             are made

by the degree of similarity.          Causal judgments     are often made as a function of the similarity           between the cause and the

actual outcomes,        such as the magnitude      of the possible causes and the magnitude           of the effect.        People initially had

difficulty accepting that something           small enough to be invisible,      such as a virus, could cause a deadly disease.                The use of

the representativeness        heuristic also makes it difficult for people to recognize when events are the result of a random

process.     Judgments      of similarity   can readily be made from small samples.              People tend to expect that every part of a

sequence, no matter how small, should appear “random,”                    leading to what is known as the Gambler’s              Fallacy.     When

flipping a coin, the average number of tails or heads in a row is two.                  Expecting every part of any sequence of coin flips

to reflect this feature, after two heads have been flipped, people act as if a tail is, as it were, overdue.     However,   if a tail

does not appear for four more flips--as     is likely to occur once in any given sequence of 100 tosses--then     people begin to

reject the notion that the coin is fair.   Similarly,   it is cliff%xlt for people to accept the degree to which stock price changes

are determined   by a random process.

1) Prospect Theory Value Function




          U    Losses                              Gains


                               MONETARY CHANGE

2) Prospect Theory Probabilty Weighting Function



                0                                   1

                        ASSESSED PROBABILITY


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